An angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.In the figure, AB is the diameter of the circle, find the value of ∠ACDSelect an answerA30ºB60ºC45ºD25º
Question
An angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.In the figure, AB is the diameter of the circle, find the value of ∠ACDSelect an answerA30ºB60ºC45ºD25º
Solution
The problem states that AB is the diameter of the circle. This means that ∠AOB is a straight angle, or 180º.
Since ∠AOB is subtended by the arc AD, the angle subtended by the same arc at any other point on the circle is half of ∠AOB.
Therefore, ∠ACD = 1/2 * ∠AOB = 1/2 * 180º = 90º.
However, none of the options A, B, C, or D match this result. There might be a mistake in the problem or the answer choices.
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